MODEL THE LONG-TERM DYNAMICS OF BODY MASS INDEX CHANGE FOLLOWING ROUX-EN-Y GASTRIC BYPASS: A SYSTEMS SCIENCE APPROACH

Purpose: We aimed to use a systems science approach to model and simulate the long-term (~25 years) dynamics of body mass index (BMI) change (ΔBMI) following Roux-en-Y Gastric Bypass (RYGB).

Method: We constructed a system dynamics model for RYGB patients, consisting of a set of ordinary differential equations, based on a validated model of human metabolism (Hall et al., 2009). This model is used to simulate continuous ΔBMI over a 25-year time horizon. To demonstrate our model, we used a typical female patient with a BMI of 45.4 kg/m² undergoing RYGB as an example. Data for her energy intake (EI) and physical activity (PA) ≤2 years after RYGB were obtained from the published data (EI=1,240 kcal/day; PA=63 min/day, Coupaye et al., 2009); and data for EI and PA >2 years after surgery were modified overtime to approximate the national averages of EI and PA for the general population with the same characteristics of this female, from the NHANES, 2009-2012. We calibrated our model by minimizing the difference between our data and published data at different time points. We then ran a Monte Carlo simulation and plotted the ΔBMI trajectory using the mean and 95% confidence interval (CI). We then compared this trajectory with a hypothetical scenario, in which EI and PA were set at the recommended level (EI=1,400 kcal/day; PA=150 min/day) throughout the 25 years after surgery.

Result: We demonstrated the projected ΔBMI trajectory for a female RYGB patient 25 years following surgery (blue curve in the Figure), contrasting to the hypothetical scenario, in which this patient constantly maintains her EI and PA at the recommended level (red curve). Our model predicted that this patient experiences a rapid BMI loss of 22.0 (95% CI: 8.7-35.2) kg/m² after 2 years, at which point the maximum BMI loss was reached. Patients regained some weight in the subsequent years. BMI loss at 5, 10, and 15 years were 9.9 (95% CI: 7.5-12.3) kg/m², 6.7 (95% CI: 4.2-9.1) kg/m², and 4.3 (95% CI: 1.7-6.9) kg/m², respectively. This is consistent with the published data.

Conclusion: Our system dynamics model can successfully predict the long-term ΔBMI trajectory for RYGB patients and project the difference in ΔBMI trajectory between recommended levels of EI and PA and those driven by patient data.